Three identical dipoles are arranged as shown below. What will be the net electric field at $P$ $\left( {k = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$?

An electric dipole of dipole moment $\vec{P}$ is placed in a uniform electric field $\vec{E}$. Which of the following statements are correct?
Statement $I$: The torque on the dipole is $\vec{\tau} = \vec{P} \times \vec{E}$
Statement $II$: The potential energy of the dipole is $U = -\vec{P} \cdot \vec{E}$
Statement $III$: The net force on the dipole is non-zero

As shown in the figure,a charge $+q$ is moved from point $A \,(r, 135^{\circ})$ to point $B \,(r, 45^{\circ})$. If the dipole moment is $p$,what is the work done by an external agent?

The distance between the two charges $+q$ and $-q$ of a dipole is $r$. On the axial line at a distance $d$ from the centre of the dipole,the electric field intensity is proportional to:

Charges are placed at the vertices of an equilateral triangle as shown in the figure. What is the resultant dipole moment?

Two electric dipoles of moment $P$ and $64 P$ are placed in opposite directions on a line at a distance of $25 \ cm$. The electric field will be zero at a point between the dipoles whose distance from the dipole of moment $P$ is.....$cm$.